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Question Number 126572 by sdfg last updated on 22/Dec/20

Answered by liberty last updated on 22/Dec/20

 ∣a^→ +b^→ ∣^2 = ∣a^→ ∣^2 +∣b^→ ∣^2 +2∣a^→ ∣∣b^→ ∣cos α          50    = 25 +25 + 2(5)(5)cos α         cos α = 0 → α=(π/2)

$$\:\mid\overset{\rightarrow} {{a}}+\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} =\:\mid\overset{\rightarrow} {{a}}\mid^{\mathrm{2}} +\mid\overset{\rightarrow} {{b}}\mid^{\mathrm{2}} +\mathrm{2}\mid\overset{\rightarrow} {{a}}\mid\mid\overset{\rightarrow} {{b}}\mid\mathrm{cos}\:\alpha\: \\ $$$$\:\:\:\:\:\:\:\mathrm{50}\:\:\:\:=\:\mathrm{25}\:+\mathrm{25}\:+\:\mathrm{2}\left(\mathrm{5}\right)\left(\mathrm{5}\right)\mathrm{cos}\:\alpha \\ $$$$\:\:\:\:\:\:\:\mathrm{cos}\:\alpha\:=\:\mathrm{0}\:\rightarrow\:\alpha=\frac{\pi}{\mathrm{2}} \\ $$

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